In the cylinder-by-cylinder air-fuel-ratio control, an air-fuel-ratio in each cylinder of an internal combustion engine is estimated based on a detection value of an air-fuel-ratio sensor disposed in a confluent portion of an exhaust gas emitted from the internal combustion engine. Based on the estimated air-fuel-ratio of each cylinder, the actual air-fuel-ratio of each cylinder is controlled. Japanese patent No. 4314573 (US-2005/0022797 A1) shows a cylinder-by-cylinder air-fuel-ratio control in which a learning value of a correction quantity (air-fuel-ratio learning value) for each cylinder is computed based on the correction quantity for each cylinder (fuel correction quantity). The learning value is stored in a backup memory. The cylinder-by-cylinder air-fuel-ratio control is executed based on the stored learning value.
In a system in which an air-fuel-ratio of each cylinder is estimated based on a detection value of an air-fuel-ratio sensor to adjust the air-fuel-ratio of each cylinder, it is likely that an air-fuel-ratio detection timing (sampling timing of air-fuel-ratio sensor output) may deviate from a proper detection timing. If the air-fuel-ratio detection timing deviates, an estimation accuracy of the air-fuel-ratio of each cylinder is deteriorated and the estimated air-fuel-ratio between cylinders does not converge even if the cylinder-by-cylinder air-fuel-ratio control is continued.
However, in the air-fuel-ratio control shown in Japanese patent No. 4314573 (US-2005/0022797 A1), even though the estimated air fuel ratios between cylinders does not converge, the learning value of the correction quantity for each cylinder is computed based on the correction quantity obtained by executing the air-fuel-ratio control. As a result, it is likely that the learning value of the correction quantity for each cylinder may be erroneously learned.